The Stacks project

Example 58.3.2. Let $G$ be a topological group. An important example will be the forgetful functor

where $\textit{Finite-}G\textit{-Sets}$ is the full subcategory of $G\textit{-Sets}$ whose objects are the finite $G$-sets. The category $G\textit{-Sets}$ of $G$-sets is defined in Definition 58.2.1.